One of my now retired former colleagues, worked on NEBO, Nuclear Engine Bomber, a program back in the 1960's. Nuclear power was converted into electrical power. The program was technically succeeding, but failed politically. It would be even worse today.

NASA and others are developing this technology for the purpose of significantly reducing the time to travel to other planets.

Don't forget that "nuke propulsion" comes in different flavors:
Nuclear reactions are used aboard spacecraft in a few ways:
1. RTGs. Small amounts of radioactive isotopes provide heat and power as they slowly decay over many years. These are used aboard deep-space probes such as Cassini.
2. Nuclear reactors. These were actually developed in the 1960s under project NERVA before it was canceled. In this design, nuclear reactors are used to superheat the engine exhaust, increasing propulsion efficiency. These have never been used on a spacecraft, although NASA's new Project Prometheus is reviving the concept for a possible mission to Europa next decade, which would involve an ion engine and a nuclear reactor.
3. Nuclear bomb propulsion. This is probably what you are talking about; using bombs to propel a spacecraft. This is definitely the least developed of the three.

The other problem is the feasibility of constructing an appropriate exhaust nozzle. Either you have to explode the bombs a good distance away from the rocket (huge waste of power), or you need a combustion chamber that can contain and direct a nuclear explosion. The walls of the chamber would have to handle both heat and mechanical stress. Some ceramics have outrageous melting points (the CRC Handbook lists Tantalum Carbide as having a melting point of 4880 Celsius!), but they have a way of being brittle. The Columbia disaster shows that high temperature resiliance and high stress resiliance are not the same thing.

The walls of the chamber would have to handle both heat and mechanical stress. Some ceramics have outrageous melting points (the CRC Handbook lists Tantalum Carbide as having a melting point of 4880 Celsius!), but they have a way of being brittle. The Columbia disaster shows that high temperature resiliance and high stress resiliance are not the same thing.

As has been pointed out materials able to withstand this service are outside current materials science. So on the pro side we have lots of energy. On the con side we have lots of energy.

Any pusher plate will have to be considered a sacrificial surface. It will be eroded and deformed by heat, it will be fatigued by shock, and very quickly become radioactive.

Equipment attached to said device will have to under go periods of great delta vee. In addition and importantly the delta accel or jerk will be extreme. Complex systems will not survive.

Due to treaties and common sense no one will use such a launch device in the atmosphere. The same goes for launching enough warheads to feed a ship of that type in space. The common consensus seems to be that sure you could do it, but no one will.

Don't forget that "nuke propulsion" comes in different flavors:Nuclear reactions are used aboard spacecraft in a few ways:1. RTGs. Small amounts of radioactive isotopes provide heat and power as they slowly decay over many years. These are used aboard deep-space probes such as Cassini.2. Nuclear reactors. These were actually developed in the 1960s under project NERVA before it was canceled. In this design, nuclear reactors are used to superheat the engine exhaust, increasing propulsion efficiency. These have never been used on a spacecraft, although NASA's new Project Prometheus is reviving the concept for a possible mission to Europa next decade, which would involve an ion engine and a nuclear reactor.3. Nuclear bomb propulsion. This is probably what you are talking about; using bombs to propel a spacecraft. This is definitely the least developed of the three.

4. Fusion propulsion. Easily the most powerful type, and likely to be viable in the next decade. The biggest problem of a fusion power generator -- that of making a self-sustaining, energenic reaction -- is not even in consideration for a thrusting reactor. Although self-sustenance is undoubtedly necessary, all that is required is a break-even reaction -- one that requires no input of energy -- and several labs have succeeded at creating these. The only trick left is to scale it up. By the way, once a fusion drive is perfected, the fuel is insanely cheap: it uses either elemental Hydrogen or Deuterium.

fusion propulsion is no where near going anything beyond theory at present. i would of course like to see a viable fusion engine, but i think you should realize that a viable power plant is required before we can really think about propulsion, and it'll be a while before we get a really good one that can be scaled down. it very well may be that fusion will not ever be used much for propulsion in space, just for power (better than antimatter because fuel can be gotten from free space). after all, antimatter propulsion is easy (relatively) once you get the antimatter itself, which we can, though in too small amounts.

fusion propulsion is no where near going anything beyond theory at present. i would of course like to see a viable fusion engine, but i think you should realize that a viable power plant is required before we can really think about propulsion, and it'll be a while before we get a really good one that can be scaled down. it very well may be that fusion will not ever be used much for propulsion in space, just for power (better than antimatter because fuel can be gotten from free space). after all, antimatter propulsion is easy (relatively) once you get the antimatter itself, which we can, though in too small amounts.

Not quite accurate: you don't need a viable fusion power plant before you can have a fusion engine. You can even have a fusion drive that requires power input (of which we have several) -- just connect a standard fission plant to it. The only problem is making it weight-efficient, which is relatively minor. And there are three major problems with antimatter: one, that it is insanely expensive; two, that it is necessarily almost impossible to store; three, that the drive is hard to design because you have to make the normal matter and antimatter collide at high speeds due to their natural repulsion for each other.

Not quite accurate: you don't need a viable fusion power plant before you can have a fusion engine. You can even have a fusion drive that requires power input (of which we have several) -- just connect a standard fission plant to it. The only problem is making it weight-efficient, which is relatively minor. And there are three major problems with antimatter: one, that it is insanely expensive; two, that it is necessarily almost impossible to store; three, that the drive is hard to design because you have to make the normal matter and antimatter collide at high speeds due to their natural repulsion for each other.

you need a viable fusion power plant for propulsion because there's no point in making something that's not energy efficient. also you can't just "connect" a fission plant to it, it's really convoluted and hard to do that, plus we don't have any real fission plants that are weight efficient for space in the first place, so that's another issue. also the reason antimatter is insanely expensive is because you have to make it in particle accelerators now which aren't made for making it so with some research a more efficient way could be found. and you don't have to make them collide at high speeds, they have the same attraction as any normal matter does, maybe more since particles have opposite charges in antimatter.

you need a viable fusion power plant for propulsion because there's no point in making something that's not energy efficient. also you can't just "connect" a fission plant to it, it's really convoluted and hard to do that, plus we don't have any real fission plants that are weight efficient for space in the first place, so that's another issue. also the reason antimatter is insanely expensive is because you have to make it in particle accelerators now which aren't made for making it so with some research a more efficient way could be found. and you don't have to make them collide at high speeds, they have the same attraction as any normal matter does, maybe more since particles have opposite charges in antimatter.

What I was saying is that you don't need a fusion reactor that works as an electricity generator. A power plant is not necessarily efficient as an engine, and vice versa. It doesn't need to be energy efficient because it can consume more energy than it produces -- hence the use of the fission reactor to provide the power to run the fusion reactor.

A major problem with antimatter is the storage: you require bulky electromagnetic assemblies in near-pure vacuum to keep the antimatter from colliding with your ship (an obvious problem). Then you have to funnel the appropriate amount of antimatter out of the storage area, into the reaction chamber, and collide it with normal matter -- all the while in even harder vacuum than that of interplanetary space.

On the other hand, a fusion reactor simply requires storage of hydrogen or deuterium, then an electrical arc or laser array to compress and superheat the hydrogen to appropriate temperatures, and a magnetic containment field and exhaust funnel. If nothing else, fusion is far less dangerous and temperamental.

Fusion is feasible in the long term and has several advantages. First, we know it works--after all, the sun still shines. The technical challenges are still formidable, even though it may well be easier to make a rocket engine than an energy generating plant. Still, you have to confine the plasma, and that's where many of the technical issues of the last 30 years have resided. Second, you have to come up with a way of getting the greatest momentum change out of the reaction. There are essentially two solutions: either you generate electricity and use it to power an accelerating grid, with some other material as a working fluid, or you expel the superheated plasma itself as a working fluid. The former requires an extra step, extra equipment, extra mass, etc., while the latter requires confinement of the jet.

The deuterium-tritium reaction now getting the most attention generates an alpha particle and a free neutron as products. The neutron carries off 80% of the energy and, being neutral, cannot be guided by electromagnetic forces, making it difficult to form an exhaust stream.